You forgot to include, as most people do, James Clerk Maxwell without whom Einstein would have remained a failed comedian working at the post Office and Tesla a tinkerer in some forgotten basement.
Posted on 07/21/2018 6:18:51 PM PDT by DUMBGRUNT
Um, ... Mathematical Physics ... as in applying Tensor Analysis.
You did not specify which form of math and Mathematical Physics was the subject of Maxwell’s field equations
Well, quaternions are used quite a bit for computer graphics...
“turned off”
Historically, in terms of development, it seems that math precedes physics, and physics precedes engineering. In a nutshell, it’s coming up with the ability to model something effectively.
As the pointy-heads play their games, they will eventually come up with something practical. Discovery and invention is not a linear progression.
Will have to look for more info on octonions.
“A New Kind of Science”
I have the book.
Usually with Wolfram the answer is - Cellular Automata.
Regardless of the question!
This is seems to be an extension of Sir William Rowan Hamilton’s quaternions (maybe?). Also Clifford Algebra’s which I know very little about other then the title. Learning something about it (maybe more then the title - Table of Contents...maybe?) is on my retirement “to do list”!
Octonions.
Won’t make my car go faster.
Grow my vegetables bigger.
Drop a deer sooner.
Kill an intruder easier.
Octonions. I have no use for them.
(But the gal is Hot!)
I don’t think I ever fully grasped what Wolfram was up to. My brief foray into differential calculus is 4+ decades behind me.
But his book is and remains a fascinating read.
Nice!
Thank you.
While crossing a bridge with his wife, Sir William Hamilton made a mathematical discovery so profound he carved it onto a stone. After 10 years of work, he had finally found a way to simultaneously rotate about multiple axis. He named his discovery Quaternions.
Although his discovery went unnoticed for a while, it wasn’t until the flight simulation and computer graphics industry that Quaternions mathematics became alive again. Quaternions are mainly used in computer graphics when a 3D character rotation is involved. Quaternions allows a character to rotate about multiple axis simultaneously, instead of sequentially as matrix rotation allows. For example, to rotate 45 degrees about the xy-axis using matrix rotations, the character must first rotate about the x-axis and then rotate about the y-axis. With quaternions this sequential process is not necessary.
Why use Quaternions to rotate a 3D character when matrices can do the same job? There are two reasons why Quaternions are preferred in computer graphics:
Matrix rotations suffer from what is known as Gimbal Lock.
Quaternions consume less memory and are faster to compute than matrices.
Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, “locking” the system into rotation in a degenerate two-dimensional space. 2
The goal to talk about quaternions is to see how they can help us rotate characters more efficiently. However, before we talk about rotations, let’s learn a bit more about quaterion arithmetics.
https://www.haroldserrano.com/blog/quaternions-in-computer-graphics
I really like that phrase. I did computer science, so there was some discrete math tossed in with that. Never did differential equations.
“Octonions. I have no use for them.”
Guessing that you are NOT reading this on TTY output.
I once had a Centronics 101A, that baby was FAST and fun.
The paper slew was sufficient to stand the paper straight up!
They were a bit heavy.
See #44 and #51.
And, yes she is ‘easy’ on the eyes.
Moreso, as you learn about her vocation and avocations.
She has some nice youtube videos.
Methinks, if you are into Wolfram, you are well past the title block.
Go for it!
Historically physics did not precede engineering.
Engineering generally preceded physics.
Engineering is fundamentally empirical. If something works, it works, and is used whether or not the reason why it works is understood. That is still the case. Physics supplies some handy formulas that are sometimes useful, or that engineers torture into usefulness, as modeling tools, but this rarely survives testing.
I think Reily has it pretty close. The Wolfram answer to any question is “Cellular Automata.
But is seems to me that he has replaced mathematics as a basis for discovering and defining “Scientific Truth” with computer programs, perhaps very simple ones, that are the basis for his Cellular Automata.
So, while I still don’t get it, I’m betting he would agree that the mathematicians have ruined physics.
But I don’t agree. At best it seems to me that Worlfram’s theories might complement traditional physics. But the idea that you can replace those quations with computer programs is a non-starter.
Also, as PIF noted: I left Maxwell off my list by name and stuck him in “others”. Very unfair of me. I made my living using his equations for a long time.
Thanks for the note InterceptPoint
Anyone ever studied the works of Townsend Brown?
The model sketch reminds me of a Moravian star.
Townsend Brown.
I can’t recall knowing about him but a quick read of his Wikipedia article tells me that I must have, at least indirectly, run into his ideas.
I miss the good old days of Anti-Gravity and UFOs.
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